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Moving Space Time Finite Element Methods For Convection Diffusion Problems
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Book Synopsis Moving Space-time Finite Element Methods for Convection-diffusion Problems by : Rafael Brigham Neves Ferreira Santos
Download or read book Moving Space-time Finite Element Methods for Convection-diffusion Problems written by Rafael Brigham Neves Ferreira Santos and published by . This book was released on 1991 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Analysis of Some Higher Order Space-Time Moving Finite Element Methods by : Maximilian Sloan Metti
Download or read book Analysis of Some Higher Order Space-Time Moving Finite Element Methods written by Maximilian Sloan Metti and published by . This book was released on 2013 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a study of an application of finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, this work analyzes finite element discretizations that employ moving meshes in order to solve linear differential equations over space-time domains. These methods can lead to significant savings in computation costs for problems having solutions that develop steep moving fronts, as moving meshes have the ability to track these fronts continuously with a high concentration of nodes; this flexibility allows for much larger time steps than standard tensor product finite elements, while maintaining high resolution of fine structures that sweep through the spatial domain. The main results are a priori and a posteriori error bounds for some moving finite element methods of high order and general time-stepping schemes. These finite element methods follow a method of lines approach for propagating the solution in time, though the error analysis places a strong emphasis on the properties inherited by the finite element aspects of the discrete problem. Another focus of this work is to determine practical and efficient schemes for adaptive meshing and mesh motion. As a result of this research, a solver has been written in C++ that is applicable to time-dependent linear convection-diffusion-reaction equations with a single dimension for the spatial.
Book Synopsis Moving Finite Element Method by : Maria do Carmo Coimbra
Download or read book Moving Finite Element Method written by Maria do Carmo Coimbra and published by CRC Press. This book was released on 2016-11-30 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.
Book Synopsis Moving Mesh Finite Element Method for Time Dependent Convection-Diffusion Problems by : Matthew Maxwell McCoy
Download or read book Moving Mesh Finite Element Method for Time Dependent Convection-Diffusion Problems written by Matthew Maxwell McCoy and published by . This book was released on 2021 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moving mesh finite element method (MM-FEM) has been a significant force in numerically approximating solutions to differential equations that otherwise exhibit spurious, artificial oscillations. This is especially true for singularly perturbed convection-diffusion problems. In the presence of vanishing molecular diffusivity, MM- FEM may not suffice. The numerical method may exhibit under-diffusive properties and other methods need to be integrated into the classic Galerkin formulation. We implement the so-called streamline upwind Petrov-Galerkin method into the adaptive moving mesh method. In particular, we investigate the computation of so-called enhanced diffusivity for spatiotemporal periodic turbulent flows. We look at the case of Brownian tracer particles, i.e. negligible inertial effects. These types of passive advection-diffusion models are used in atmospheric models with turbulent diffusion, so-called Benard-advection cells, and porous materials, along with many other areas of science and engineering. As molecular diffusivity decreases, interior and boundary layers propagate along the streamlines. Once spurious oscillations are present, they too will propagate along the streamlines. Thus, specialized numerical methods are needed in order to resolve these areas of the domain where large gradients are present. The discrete maximum principle is also investigated for general anisotropic time dependent convection-diffusion equations. We obtain lower and upper bounds for time steps as well as obtain conditions on the mass and stiffness matrices resulting from the SUPG formulation. Our approach depends on two meshes and taking into consideration two diffusion matrices and applying metric intersection.
Book Synopsis Space-Time Methods by : Ulrich Langer
Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
Author :American Society of Mechanical Engineers. Applied Mechanics Division Publisher : ISBN 13 : Total Pages : pages Book Rating :4.:/5 (277 download)
Book Synopsis Finite Element Methods for Convection Dominated Flows by : American Society of Mechanical Engineers. Applied Mechanics Division
Download or read book Finite Element Methods for Convection Dominated Flows written by American Society of Mechanical Engineers. Applied Mechanics Division and published by . This book was released on 1979 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Galerkin Finite Element Methods for Parabolic Problems by : Vidar Thomee
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Book Synopsis Geometrically Unfitted Finite Element Methods and Applications by : Stéphane P. A. Bordas
Download or read book Geometrically Unfitted Finite Element Methods and Applications written by Stéphane P. A. Bordas and published by Springer. This book was released on 2018-03-13 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
Book Synopsis Moving Finite Element Methods by Use of Space-time Elements by : Peter Hansbo
Download or read book Moving Finite Element Methods by Use of Space-time Elements written by Peter Hansbo and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Space-time Finite Element Method for Fluid-structure Interaction by : Arif Masud
Download or read book A Space-time Finite Element Method for Fluid-structure Interaction written by Arif Masud and published by . This book was released on 1993 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Book Synopsis The Finite Element Method for Initial Value Problems by : Karan S. Surana
Download or read book The Finite Element Method for Initial Value Problems written by Karan S. Surana and published by CRC Press. This book was released on 2017-10-17 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathematical details as well as applications of space-time coupled and space-time decoupled finite element methods for IVPs. Space-time operator classification, space-time methods of approximation, and space-time calculus of variations are used to establish unconditional stability of space-time methods during the evolution. Space-time decoupled methods are also presented with the same rigor. Stability of space-time decoupled methods, time integration of ODEs including the finite element method in time are presented in detail with applications. Modal basis, normal mode synthesis techniques, error estimation, and a posteriori error computations for space-time coupled as well as space-time decoupled methods are presented. This book is aimed at a second-semester graduate level course in FEM.
Book Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson
Download or read book Numerical Solution of Partial Differential Equations by the Finite Element Method written by Claes Johnson and published by Courier Corporation. This book was released on 2012-05-23 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.
Book Synopsis An Eulerian Space-time Finite Element Method for Diffusion Problems on Evolving Surfaces by : Maksim A. Olšanskij
Download or read book An Eulerian Space-time Finite Element Method for Diffusion Problems on Evolving Surfaces written by Maksim A. Olšanskij and published by . This book was released on 2013 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Element Methods for Flow Problems by : Jean Donea
Download or read book Finite Element Methods for Flow Problems written by Jean Donea and published by John Wiley & Sons. This book was released on 2003-06-02 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Die Finite-Elemente-Methode, eines der wichtigsten in der Technik verwendeten numerischen Näherungsverfahren, wird hier gründlich und gut verständlich, aber ohne ein Zuviel an mathematischem Formalismus abgehandelt. Insbesondere geht es um die Anwendung der Methode auf Strömungsprobleme. Alle wesentlichen aktuellen Forschungsergebnisse wurden in den Band aufgenommen; viele davon sind bisher nur verstreut in der Originalliteratur zu finden.
Book Synopsis Finite Element Methods for Convection Dominated Flows by : Thomas J. R. Hughes
Download or read book Finite Element Methods for Convection Dominated Flows written by Thomas J. R. Hughes and published by . This book was released on 1979 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advanced Finite Element Methods with Applications by : Thomas Apel
Download or read book Advanced Finite Element Methods with Applications written by Thomas Apel and published by Springer. This book was released on 2019-06-28 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.
